Integrating Logarithmic Functions

The video tutorial explains how to find the area under the curve of the function y = log x using integrals. It highlights common mistakes students make when integrating logarithmic functions, such as confusing differentiation with integration. The tutorial introduces the concept of using exponential functions to solve integration problems, demonstrating how to rewrite the function in terms of y and integrate with respect to y. The video concludes with a step-by-step solution to the integration problem, emphasizing the importance of understanding exponential and logarithmic laws.

What is the integral setup to find the area under the curve y = log x from x = 1 to x = 3?

• ∫ from 0 to 3 of 1/x dx

• ∫ from 1 to 3 of 1/x dx

• ∫ from 0 to 3 of log x dx

• ∫ from 1 to 3 of log x dx

What is a common mistake students make when trying to integrate log x?

• Forgetting to include dx

• Differentiating instead of integrating

• Using the wrong boundaries

• Using pi in the calculation

How can the function y = log x be rewritten to facilitate integration?

• x = e^y

• y = e^x

• x = ln(y)

• y = ln(x)

When integrating with respect to y, what is the lower boundary for the integral?

• log 3

• 1

• 0

• 3

What is the upper boundary for the integral when integrating with respect to y?

• 0

• 1

• 3

• log 3

What is the width of the rectangle used in the area calculation?

• 3

• log 3

• 1

• e

What is the height of the rectangle used in the area calculation?

• log 3

• e

• 3

• 1

What is the primitive of e^y when integrating with respect to y?

• ln(y)

• e^y

• y^e

• 1/e^y

What is the result of e^(log 3)?

• log 3

• 3

• e

• 1

What is the final step in finding the area under the curve?

• Subtracting the area under the curve from the rectangle

• Adding the areas of two rectangles

• Multiplying the width and height of the rectangle

• Dividing the area by the width of the rectangle